To find the radius of a spherical ball given its volume, we can use the formula for the volume of a sphere:
[tex]\[ V = \frac{4}{3} \pi r^3 \][/tex]
### Step-by-Step Solution:
1. Identify the Given Values:
- Volume ([tex]\( V \)[/tex]) of the ball is [tex]\( 5000 \, \text{cm}^3 \)[/tex].
- The value of [tex]\( \pi \)[/tex] is [tex]\( 3.14 \)[/tex].
2. Write the Volume Formula:
[tex]\[ 5000 = \frac{4}{3} \pi r^3 \][/tex]
3. Rearrange the Formula to Solve for [tex]\( r^3 \)[/tex]:
Multiply both sides by [tex]\( \frac{3}{4} \)[/tex] to isolate [tex]\( r^3 \)[/tex]:
[tex]\[ r^3 = \frac{3 \cdot 5000}{4 \pi} \][/tex]
4. Substitute the Value of [tex]\( \pi \)[/tex]:
[tex]\[ r^3 = \frac{3 \cdot 5000}{4 \cdot 3.14} \][/tex]
5. Calculate [tex]\( r^3 \)[/tex]:
[tex]\[ r^3 = \frac{15000}{12.56} \][/tex]
[tex]\[ r^3 \approx 1194.2675159235669 \][/tex]
6. Solve for [tex]\( r \)[/tex]:
Take the cube root of both sides to find [tex]\( r \)[/tex]:
[tex]\[ r = \sqrt[3]{1194.2675159235669} \][/tex]
[tex]\[ r \approx 10.609637360523415 \][/tex]
7. Round to One Decimal Place:
We round the result to one decimal place:
[tex]\[ r \approx 10.6 \, \text{cm} \][/tex]
### Final Answer:
The radius of the spherical ball is approximately [tex]\( 10.6 \, \text{cm} \)[/tex].
